"He didn't priority board. He didn't take a seat upgrade. He waited like everyone else, and he sat in the back," Fox told the Dallas News.

Fox and Lee described Kelly chatting with fellow passengers and taking pictures with employees.

"On Southwest there is no second class, and every seat is great," Kelly said after the flight.

Scott Mlyn | CNBC

Gary Kelly, CEO, Southwest Airlines

Kelly may be unassuming, but that doesn't mean his management style escapes notice. Job search site Glassdoor named Kelly one of the highest-rated CEOs, and Southwest was named one of the best places to work in 2017.

When Glassdoor asked employees what advice they would give management, one anonymous staff member responded, "Quit being so darn nice and accommodating.

In a "Mad Money" interview with CNBC's Jim Cramer, Kelly said the company has never laid off an employee or cut pay since it started operating in 1972. He attributed Southwest's continued profit growth to a great work culture.

"There is a lot to a culture, and it's easier to have a strong culture if you feel like you're a champion. And that's the way our employees feel," he said.